Playground.ipynb

{
 "cells": [
  {
   "cell_type": "code",
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   "metadata": {
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     "shell.execute_reply": "2024-02-23T09:46:18.671888Z"
    }
   },
   "outputs": [],
   "source": [
    "from modandcrypt import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Crittografia a chiave simmetrica\n",
    "\n",
    "## Monoalfabetica\n",
    "\n",
    "Passo passo, usando `a_posizioni` e `da_posizioni` per passare dalle lettere alle loro posizioni e `orologio_somma` per fare la somma come sull'orologio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.674400Z",
     "iopub.status.busy": "2024-02-23T09:46:18.674226Z",
     "iopub.status.idle": "2024-02-23T09:46:18.677749Z",
     "shell.execute_reply": "2024-02-23T09:46:18.677414Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'QUESTO E IN CHIARO'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = semplifica(\"Questo è in chiaro\")\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.695172Z",
     "iopub.status.busy": "2024-02-23T09:46:18.695025Z",
     "iopub.status.idle": "2024-02-23T09:46:18.697929Z",
     "shell.execute_reply": "2024-02-23T09:46:18.697603Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[16, 20, 4, 18, 19, 14, 26, 4, 26, 8, 13, 26, 2, 7, 8, 0, 17, 14]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_p = a_posizioni(p)\n",
    "pos_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.699556Z",
     "iopub.status.busy": "2024-02-23T09:46:18.699430Z",
     "iopub.status.idle": "2024-02-23T09:46:18.701856Z",
     "shell.execute_reply": "2024-02-23T09:46:18.701491Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'E'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = semplifica(\"è\")\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.703479Z",
     "iopub.status.busy": "2024-02-23T09:46:18.703272Z",
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     "shell.execute_reply": "2024-02-23T09:46:18.705501Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_k = a_posizioni(k)\n",
    "pos_k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.707477Z",
     "iopub.status.busy": "2024-02-23T09:46:18.707273Z",
     "iopub.status.idle": "2024-02-23T09:46:18.709705Z",
     "shell.execute_reply": "2024-02-23T09:46:18.709356Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[20, 24, 8, 22, 23, 18, 2, 8, 2, 12, 17, 2, 6, 11, 12, 4, 21, 18]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_c = orologio_somma(pos_p, pos_k)\n",
    "pos_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.711379Z",
     "iopub.status.busy": "2024-02-23T09:46:18.711186Z",
     "iopub.status.idle": "2024-02-23T09:46:18.713511Z",
     "shell.execute_reply": "2024-02-23T09:46:18.713148Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'UYIWXSCICMRCGLMEVS'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = da_posizioni(pos_c)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.715232Z",
     "iopub.status.busy": "2024-02-23T09:46:18.715005Z",
     "iopub.status.idle": "2024-02-23T09:46:18.717413Z",
     "shell.execute_reply": "2024-02-23T09:46:18.717115Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Y'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_inv = inverti(k)\n",
    "k_inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.718941Z",
     "iopub.status.busy": "2024-02-23T09:46:18.718769Z",
     "iopub.status.idle": "2024-02-23T09:46:18.721172Z",
     "shell.execute_reply": "2024-02-23T09:46:18.720777Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'QUESTO E IN CHIARO'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_inv_pos = a_posizioni(k_inv)\n",
    "da_posizioni(orologio_somma(pos_c, k_inv_pos))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora in un solo passaggio con `cifra` e `decifra`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.722752Z",
     "iopub.status.busy": "2024-02-23T09:46:18.722631Z",
     "iopub.status.idle": "2024-02-23T09:46:18.725625Z",
     "shell.execute_reply": "2024-02-23T09:46:18.725255Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───┬──────┬──────┬─────┬──────┬──────┬──────┬─────┬─────┬─────┬──────┬──────┬─────┬─────┬──────┬──────┬─────┬──────┬──────┐\n",
      "│ \u001b[1mp\u001b[0m │ Q:16 │ U:20 │ E:4 │ S:18 │ T:19 │ O:14 │ :26 │ E:4 │ :26 │ I:8  │ N:13 │ :26 │ C:2 │ H:7  │ I:8  │ A:0 │ R:17 │ O:14 │\n",
      "├───┼──────┼──────┼─────┼──────┼──────┼──────┼─────┼─────┼─────┼──────┼──────┼─────┼─────┼──────┼──────┼─────┼──────┼──────┤\n",
      "│ \u001b[1mk\u001b[0m │ E:4  │ E:4  │ E:4 │ E:4  │ E:4  │ E:4  │ E:4 │ E:4 │ E:4 │ E:4  │ E:4  │ E:4 │ E:4 │ E:4  │ E:4  │ E:4 │ E:4  │ E:4  │\n",
      "├───┼──────┼──────┼─────┼──────┼──────┼──────┼─────┼─────┼─────┼──────┼──────┼─────┼─────┼──────┼──────┼─────┼──────┼──────┤\n",
      "│ \u001b[1mc\u001b[0m │ U:20 │ Y:24 │ I:8 │ W:22 │ X:23 │ S:18 │ C:2 │ I:8 │ C:2 │ M:12 │ R:17 │ C:2 │ G:6 │ L:11 │ M:12 │ E:4 │ V:21 │ S:18 │\n",
      "└───┴──────┴──────┴─────┴──────┴──────┴──────┴─────┴─────┴─────┴──────┴──────┴─────┴─────┴──────┴──────┴─────┴──────┴──────┘\n"
     ]
    }
   ],
   "source": [
    "c = cifra(p, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.727283Z",
     "iopub.status.busy": "2024-02-23T09:46:18.727080Z",
     "iopub.status.idle": "2024-02-23T09:46:18.728999Z",
     "shell.execute_reply": "2024-02-23T09:46:18.728628Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UYIWXSCICMRCGLMEVS\n"
     ]
    }
   ],
   "source": [
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.730651Z",
     "iopub.status.busy": "2024-02-23T09:46:18.730446Z",
     "iopub.status.idle": "2024-02-23T09:46:18.732966Z",
     "shell.execute_reply": "2024-02-23T09:46:18.732600Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐\n",
      "│ \u001b[1mc\u001b[0m │ U:20 │ Y:24 │ I:8  │ W:22 │ X:23 │ S:18 │ C:2  │ I:8  │ C:2  │ M:12 │ R:17 │ C:2  │ G:6  │ L:11 │ M:12 │ E:4  │ V:21 │ S:18 │\n",
      "├───┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤\n",
      "│ \u001b[1mk\u001b[0m │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │ Y:24 │\n",
      "├───┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤\n",
      "│ \u001b[1mp\u001b[0m │ Q:16 │ U:20 │ E:4  │ S:18 │ T:19 │ O:14 │ :26  │ E:4  │ :26  │ I:8  │ N:13 │ :26  │ C:2  │ H:7  │ I:8  │ A:0  │ R:17 │ O:14 │\n",
      "└───┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘\n"
     ]
    }
   ],
   "source": [
    "p = decifra(c, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.734617Z",
     "iopub.status.busy": "2024-02-23T09:46:18.734452Z",
     "iopub.status.idle": "2024-02-23T09:46:18.736379Z",
     "shell.execute_reply": "2024-02-23T09:46:18.736001Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "QUESTO E IN CHIARO\n"
     ]
    }
   ],
   "source": [
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polialfabetica\n",
    "\n",
    "In realtà non cambia nulla, perché `orologio_somma` ripete tante volte la chiave quanto serve ad avere un valore per ogni lettera."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.738036Z",
     "iopub.status.busy": "2024-02-23T09:46:18.737803Z",
     "iopub.status.idle": "2024-02-23T09:46:18.740637Z",
     "shell.execute_reply": "2024-02-23T09:46:18.740292Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───┬──────┬──────┬──────┬──────┬─────┬──────┬─────┬──────┬──────┬──────┬──────┬─────┬──────┬──────┬─────┬──────┬─────┬──────┬──────┬─────┬──────┐\n",
      "│ \u001b[1mp\u001b[0m │ C:2  │ O:14 │ S:18 │ I:8  │ :26 │ E:4  │ :26 │ P:15 │ O:14 │ L:11 │ I:8  │ A:0 │ L:11 │ F:5  │ A:0 │ B:1  │ E:4 │ T:19 │ I:8  │ C:2 │ O:14 │\n",
      "├───┼──────┼──────┼──────┼──────┼─────┼──────┼─────┼──────┼──────┼──────┼──────┼─────┼──────┼──────┼─────┼──────┼─────┼──────┼──────┼─────┼──────┤\n",
      "│ \u001b[1mk\u001b[0m │ V:21 │ E:4  │ R:17 │ M:12 │ E:4 │ V:21 │ E:4 │ R:17 │ M:12 │ E:4  │ V:21 │ E:4 │ R:17 │ M:12 │ E:4 │ V:21 │ E:4 │ R:17 │ M:12 │ E:4 │ V:21 │\n",
      "├───┼──────┼──────┼──────┼──────┼─────┼──────┼─────┼──────┼──────┼──────┼──────┼─────┼──────┼──────┼─────┼──────┼─────┼──────┼──────┼─────┼──────┤\n",
      "│ \u001b[1mc\u001b[0m │ X:23 │ S:18 │ H:7  │ U:20 │ C:2 │ Z:25 │ C:2 │ E:4  │ :26  │ P:15 │ B:1  │ E:4 │ A:0  │ R:17 │ E:4 │ W:22 │ I:8 │ I:8  │ U:20 │ G:6 │ H:7  │\n",
      "└───┴──────┴──────┴──────┴──────┴─────┴──────┴─────┴──────┴──────┴──────┴──────┴─────┴──────┴──────┴─────┴──────┴─────┴──────┴──────┴─────┴──────┘\n"
     ]
    }
   ],
   "source": [
    "c = cifra(\"Così è polialfabetico\", \"verme\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.742267Z",
     "iopub.status.busy": "2024-02-23T09:46:18.742103Z",
     "iopub.status.idle": "2024-02-23T09:46:18.744000Z",
     "shell.execute_reply": "2024-02-23T09:46:18.743624Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XSHUCZCE PBEAREWIIUGH\n"
     ]
    }
   ],
   "source": [
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.745702Z",
     "iopub.status.busy": "2024-02-23T09:46:18.745496Z",
     "iopub.status.idle": "2024-02-23T09:46:18.748089Z",
     "shell.execute_reply": "2024-02-23T09:46:18.747716Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌───┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬─────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐\n",
      "│ \u001b[1mc\u001b[0m │ X:23 │ S:18 │ H:7  │ U:20 │ C:2  │ Z:25 │ C:2  │ E:4  │ :26  │ P:15 │ B:1 │ E:4  │ A:0  │ R:17 │ E:4  │ W:22 │ I:8  │ I:8  │ U:20 │ G:6  │ H:7  │\n",
      "├───┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼─────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤\n",
      "│ \u001b[1mk\u001b[0m │ H:7  │ Y:24 │ L:11 │ Q:16 │ Y:24 │ H:7  │ Y:24 │ L:11 │ Q:16 │ Y:24 │ H:7 │ Y:24 │ L:11 │ Q:16 │ Y:24 │ H:7  │ Y:24 │ L:11 │ Q:16 │ Y:24 │ H:7  │\n",
      "├───┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼─────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤\n",
      "│ \u001b[1mp\u001b[0m │ C:2  │ O:14 │ S:18 │ I:8  │ :26  │ E:4  │ :26  │ P:15 │ O:14 │ L:11 │ I:8 │ A:0  │ L:11 │ F:5  │ A:0  │ B:1  │ E:4  │ T:19 │ I:8  │ C:2  │ O:14 │\n",
      "└───┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴─────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘\n"
     ]
    }
   ],
   "source": [
    "p = decifra(c, \"verme\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.749696Z",
     "iopub.status.busy": "2024-02-23T09:46:18.749549Z",
     "iopub.status.idle": "2024-02-23T09:46:18.751450Z",
     "shell.execute_reply": "2024-02-23T09:46:18.751069Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "COSI E POLIALFABETICO\n"
     ]
    }
   ],
   "source": [
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Crittoanalisi\n",
    "\n",
    "Proviamo con l'inglese, sempre usando [Project Gutenberg](https://dev.gutenberg.org/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:18.753065Z",
     "iopub.status.busy": "2024-02-23T09:46:18.752907Z",
     "iopub.status.idle": "2024-02-23T09:46:20.020711Z",
     "shell.execute_reply": "2024-02-23T09:46:20.018991Z"
    }
   },
   "outputs": [],
   "source": [
    "HAMLET = da_gutenberg('https://dev.gutenberg.org/cache/epub/1524/pg1524.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.025268Z",
     "iopub.status.busy": "2024-02-23T09:46:20.024994Z",
     "iopub.status.idle": "2024-02-23T09:46:20.131070Z",
     "shell.execute_reply": "2024-02-23T09:46:20.130610Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAGdCAYAAACPX3D5AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAcy0lEQVR4nO3deXDU9f348VdCOLQEvCgWCKCiYKXSWmvV9itEoQkFi8q0tFWLQqetIupoxastVlHxqlVQvIDYYq3V1qNYkEKJRWHAjuIxjXiBRYHxQg4PFPP5/eEkPyJHdiOQwPvxmNk/srvvz+e9m+zmmfd+NluQZVkWAECyCht7AgBA4xIDAJA4MQAAiRMDAJA4MQAAiRMDAJA4MQAAiRMDAJC4olyuVF1dHcuWLYvi4uIoKCjY1nMCALaCLMtizZo10aFDhygs3Pzf/znFwLJly6KkpGSrTQ4A2H6WLl0anTp12uzlOcVAcXFx7cbatGmzdWYGAGxTq1evjpKSktrf45uTUwzUvDTQpk0bMQAAO5j6XuJ3ACEAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDicvoIYwBIRdcLHs57zJKxA7bBTLYfKwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkDgxAACJEwMAkLiixp4AEV0veDjvMUvGDtgGMwEgRVYGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxRY09AYCdSdcLHs57zJKxA7bBTCB3VgYAIHFiAAASJwYAIHFiAAASJwYAIHFiAAASJwYAIHFiAAASJwYAIHFiAAASJwYAIHFiAAAS54OKgFo+ZAfSZGUAABInBgAgcWIAABInBgAgcWIAABInBgAgcWIAABInBgAgcWIAABInBgAgcWIAABInBgAgcWIAABInBgAgcWIAABInBgAgcWIAABJX1NgTiIjoesHDeY9ZMnbANpgJAKTHygAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDimsRHGIOPsQZoPFYGACBxYgAAEudlAthJeKkFaCgrAwCQODEAAIkTAwCQOMcMAGwg32MvHHfBzsDKAAAkzsoAW4Uj2QF2XGIA2GmIUmgYLxMAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOKKGnsCALAz6XrBw3mPWTJ2wDaYSe6sDABA4sQAACTOywSwleyIS4MAEVYGACB5YgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEicGACBxYgAAEueDirYCH1ADwI7MygAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJM7/GQBoQvzfEhqDlQEASJwYAIDEiQEASJwYAIDEOYAQmggHjgGNxcoAACRODABA4sQAACRODABA4sQAACRODABA4sQAACRODABA4sQAACRODABA4sQAACTOZxMA0KT4nI7tz8oAACTOykCoUIAang/TZGUAABInBgAgcV4m2ElY2gOgoawMAEDixAAAJM7LBESElxkAUmZlAAASJwYAIHFiAAASJwYAIHEOIAS2Ggeiwo7JygAAJE4MAEDixAAAJG6nOGbA65QA0HBWBgAgcWIAABInBgAgcWIAABInBgAgcWIAABInBgAgcTvF/xmArcH/qwBSJQYAdiKilobwMgEAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDixAAAJE4MAEDifFARO418P6DFh7M0PT5kZ+fg+7jjySkGsiyLiIjVq1dvk0lUr3s/7zEbziX18U1hDo09viHbcB+6Dz47viHbcB82vfug5+hH8h7/3G/Lttr+t8Z9uLXUbLfm9/jmFGT1XSMiXnvttSgpKdk6MwMAtqulS5dGp06dNnt5TjFQXV0dy5Yti+Li4igoKNiqE9yc1atXR0lJSSxdujTatGmzw41vCnNo7PFNYQ47+vimMIfGHt8U5rCjj28Kc2js8U1hDlvjNuQry7JYs2ZNdOjQIQoLN3+YYE4vExQWFm6xKLalNm3afK47rbHHN4U5NPb4pjCHHX18U5hDY49vCnPY0cc3hTk09vimMIetcRvy0bZt23qv490EAJA4MQAAiWuyMdCyZcsYPXp0tGzZcocc3xTm0Njjm8IcdvTxTWEOjT2+KcxhRx/fFObQ2OObwhy2xm3YVnI6gBAA2Hk12ZUBAGD7EAMAkDgxAACJ89kEALAFP//5z+OQQw6JL3/5y/Hee+9FeXl5Y09pq2uSKwPz5s2LZs2axYAB+X9wxSmnnBIFBQW1pz333DPKy8vjmWeeyXkbK1asiJEjR8a+++4bLVu2jJKSkjj22GNj1qxZee2/efPm0b59++jXr19MmjQpqqurG3Qbak75/ABubhsvvfRSTuNXrFgRZ511VnTr1i1atWoV7du3j29961sxYcKEeP/9Lf/f7VNOOSWOO+64jc6vrKyMgoKCePfdd/O6HZva1rYev6lx9913X7Rq1Squu+66bb7vgoKC+MUvfrHRZSNGjIiCgoI45ZRTctrG2LFj65z/wAMP5PxfRJcuXRrDhg2LDh06RIsWLaJLly5x1llnxdtvv533bSkoKIgWLVpEt27d4tJLL43169fnvI2G+uxjcZ999olRo0bFhx9+mPM23nzzzTjttNOic+fO0bJly9h7772jrKwsHn/88XrHburxt+HpkksuqXcbffr0ibPPPnuj8ysqKmK33Xbb4thjjz12s88Zc+bMiYKCgk0+L95yyy1RXFxc53u0du3aaN68efTp06fOdWse0y+//PIm9/PJJ5/EkUceGSeccEKd81etWhUlJSVx8cUXb/E2ZFkWffv2jbKyso0uu/nmm2O33XaL1157bbPja+a3uVNpaWm9+587d27MmjUrrr766pg5c2bsu+++Wxyzo2qSMTBx4sQYOXJk/Pvf/45ly5blPb68vDyWL18ey5cvj1mzZkVRUVEMHDgwp7FLliyJr3/96/Gvf/0rrrnmmnj22Wdj+vTpUVpaGiNGjMhr/0uWLIlp06ZFaWlpnHXWWTFw4MCcnwQ3vA01p7vvvjunsVvaxj777FPvuFdeeSW+9rWvxYwZM+KKK66Ip556KubNmxejRo2KqVOnxsyZM/Oax87gjjvuiBNPPDEmTJgQ55577jbfX0lJSfz5z3+ODz74oPa8Dz/8MP70pz9F586dc9pGq1at4qqrroqVK1fmvf9XXnklDj300HjxxRfj7rvvjpdeeiluueWWmDVrVhxxxBHxzjvv5Lytmp/DF198Mc4999y45JJL4pprrslp7OcNkpp9v/LKK3H99dfHrbfeGqNHj8557oMHD46nnnoq7rzzznjhhRfioYceij59+uS0/w0fd7///e+jTZs2dc775S9/mfM8GmL48OHxz3/+c5O/LCdPnhyHHnpoHHzwwRtdVlpaGmvXro3//Oc/tefNmTMn9t5775g/f36dmJo9e3Z07tw59ttvv03OoVmzZlFRURHTp0+Pu+66q/b8kSNHxh577FHv96KgoCAmT54c8+fPj1tvvbX2/MWLF8eoUaNi3LhxW/zvuEceeeRGz4HLly+PW2+9NQoKCuL000/f4v7PPffcePjhh2OXXXaJk08+OX7729/GAQccsMUxO6ysiVmzZk3WunXr7Pnnn8+GDBmSXX755XmNHzp0aDZo0KA6582ZMyeLiOyNN96od3z//v2zjh07ZmvXrt3ospUrVzZo/1mWZbNmzcoiIrv99tsbvI18fJ5tlJWVZZ06ddrkfZBlWVZdXd2gfc+ePTuLiJzux/q2ta3Hbzjuqquuylq1apX97W9/26777tmzZzZlypTa8++6667s4IMPzgYNGpQNHTq03m0MHDgw69GjR3beeefVnn///fdnuTzsy8vLs06dOmXvv/9+nfOXL1+e7brrrtkvfvGLvG7Lhvr165cdfvjh9Y59+eWXsy9+8YvZt7/97ayysjJ79dVXs3/84x/ZQQcdlO2///7Z22+/nfe+TzjhhOxrX/taTnNfuXJlFhFZZWVlTtffksmTJ2dt27bNe1zv3r2zs846q0Hb+/jjj7P27dtnl112WZ3za55jJ0yYsNmxX/rSl7Irr7yy9utRo0ZlI0aMyA488MBs9uzZtecfddRR9f4sZlmW3XDDDdnuu++eLVu2LHvggQey5s2bZwsXLqx3XI2KioqsdevW2SuvvJJVV1dnpaWl2fHHH5/z+A3997//zYqLi7OLL7445zG9e/fOzj///GzYsGFZcXFx1q5du+zSSy9t0P6bqia3MvCXv/wlevToEd27d4+TTjopJk2aVO9HL27J2rVrY8qUKdGtW7fYc889t3jdd955J6ZPnx4jRoyIL3zhCxtdXt+y3JYcffTR0atXr/jb3/7W4G1sD2+//XbMmDFjs/dBRGy3D6tqCs4///y47LLLYurUqXH88cdv130PGzYsJk+eXPv1pEmT4tRTT815fLNmzeKKK66IcePGbXEp9bPeeeedeOSRR+L000+PXXbZpc5le++9d5x44olxzz33NPhxucsuu8RHH31U7/VGjBgRLVq0iBkzZkTv3r2jc+fO0b9//5g5c2a8/vrr9S4xf9Zzzz0Xc+fOjRYtWuR0/datW0fr1q3jgQceiHXr1uW1r6agqKgofvKTn0RFRUWd79W9994bn3zySfzoRz/a7NjS0tKYPXt27dezZ8+OPn36RO/evWvP/+CDD2L+/Pn1LrVHfLoS0KtXrzj55JPjZz/7WfzmN7+JXr165Xxbhg4dGsccc0wMGzYsxo8fH88991ydlYJcvfvuuzFo0KDo06dPXHbZZXmNvemmm6Jz587x7LPPxrhx42Ls2LHxxz/+MefxCxYs2Oi8RYsWxUEHHRRPP/10XnPZFppcDEycODFOOumkiPh0iW/VqlXx6KOP5rWNqVOn1j6Qi4uL46GHHop77rlni5/YFBHx0ksvRZZl0aNHjwbPf0t69OgRS5Ysyem6G96GmtMVV1yR1/4+u43vf//79Y6puQ+6d+9e5/y99tqrdjvnn39+g+bfv3//vObf2KZNmxZXX311PPjgg3HMMcds9/2fdNJJ8dhjj8Wrr74ar776ajz++OO1j41cHX/88fHVr341r6XxF198MbIsiwMPPHCTlx944IGxcuXKePPNN/OaS5ZlMXPmzHjkkUfi6KOP3uJ1t1aQ1PwctmrVKr7yla/EG2+8Eeedd15O8y0qKoqKioq48847Y7fddotvfetbcdFFF+V1/FFjGzZsWLz88st1nkMnT54cgwcP3uKH15SWlsbjjz8e69evjzVr1sRTTz0VvXv3jqOOOioqKysj4tNju9atW5dTDBQUFMSECRNi1qxZ0b59+7jgggvyvi233XZbPPfcc3H22WfHbbfdFu3atctrfHV1dfz4xz+OoqKiuOuuu/L+o6Znz54xevTo6NKlSwwZMiRGjBgRN9xwQ05jzz333DjuuOM2Ot5qn332ib59+8Y555yT11y2hSYVA4sWLYoFCxbUFmtRUVEMGTIkJk6cmNd2SktLY+HChbFw4cJYsGBBlJWVRf/+/ePVV1/d4rjPswKRiyzLcv4B3PA21Jw2dUBZPtu48cYbGzLtiPi0ahcuXBgHHXRQTn8lbWr+d9xxR4P33xgOPvjg6Nq1a4wePTrWrl273fffrl27GDBgQFRUVMTkyZNjwIABsddee+W9nauuuiruvPPOqKqqymvc1no8bPgLuX///jFkyJB6D57bWkFS83M4f/78GDp0aJx66qkxePDgnOc+ePDgWLZsWTz00ENRXl4elZWVccghh0RFRUXO22hMPXr0iCOPPDImTZoUEZ/G/pw5c2L48OFbHNenT59477334oknnog5c+bEAQccEO3atYvevXvXHjdQWVkZ++67b87HsEyaNCl23XXXWLx4cV4rVTW++MUvxs9//vM48MADG3Rg7kUXXRTz5s2LBx98MIqLi/Mef8QRR9T5+sgjj4znn3++3nEXX3xxVFRUxCOPPBK77rpr7fk1vw86duzYKM8vn9Wk3lo4ceLEWL9+fXTo0KH2vCzLomXLljF+/PicPoYxIuILX/hCdOvWrfbrO+64I9q2bRu33357jBkzZrPj9t9//ygoKMjpG9wQVVVVOR3AF7HxbWiIhmyjW7duUVBQEIsWLapzfs0RtJ/9Ky2ffTfkCaAxdezYMe67774oLS2N8vLymDZtWoOeRD6PYcOGxRlnnBERny5TNsRRRx0VZWVlceGFF9b7LoSI//8zUFVVtcmXRqqqqmL33XfP+S+z0tLSmDBhQrRo0SI6dOgQRUW5P+3UFyT1Lflv+HM4adKk6NWrV0ycOLHeX4YbatWqVfTr1y/69esXv/71r+OnP/1pjB49Oqf78vNq06ZNrFq1aqPz33333ZyfD4cPHx4jR46Mm266KSZPnhz77bdf9O7de4tjunXrFp06dYrZs2fHypUra6/foUOHKCkpiblz58bs2bPrXeGpMXfu3Lj++utjxowZMWbMmBg+fHjMnDkz77/Oi4qK8vr5qfHnP/85rr322nj44Ydj//33z3t8xMYvjxYWFkZ1dfUW/8ibN29e7Yrupg7WjPj0Z/Tee+9t0Jy2piazMrB+/fr4wx/+ENddd12dvyaffvrp6NChQ95H0m+ooKAgCgsL6xyZvSl77LFHlJWVxU033RTvvffeRpfn85a4z/rXv/4Vzz77bF5/lTSGPffcM/r16xfjx4/f5H2Qmi5dusSjjz4aK1asiPLy8lizZs123X95eXl89NFH8fHHH2/y7VW5Gjt2bPz973+PefPm1Xvdmp+Bm2++eaPHzIoVK+Kuu+6KIUOG5PxEXvMLuXPnzjk/kW8YJJtSVVUV7dq1y+s4nsLCwrjoooviV7/6Vb3PBVtS817z7aF79+7x5JNPbnT+k08+mfNR7T/4wQ+isLAw/vSnP8Uf/vCHGDZsWE7fu9LS0qisrIzKyso6byk86qijYtq0abFgwYKcXiJ4//3345RTTonTTjstSktLY+LEibFgwYK45ZZbcpr/57Vw4cIYPnx4jB079nM9hjZ8d0VExBNPPFH7B+TmHHbYYfHDH/4w9thjj5g1a1ZUVVVtdHr99debxEuoTSYGpk6dGitXrozhw4dHz54965wGDx6c10sF69atixUrVsSKFSuiqqoqRo4cGWvXro1jjz223rE33XRTfPLJJ3HYYYfFX//613jxxRejqqoqbrzxxo2Wierb/+uvvx5PPvlkXHHFFTFo0KAYOHBg/OQnP8n7NtSc3nrrrZzGfl4333xzrF+/Pg499NC45557oqqqKhYtWhRTpkyJ559/Ppo1a7Zd5tFUlJSURGVlZbzxxhtRVlYWq1evznnsqlWrNnq5ZOnSpTmPb9asWVRVVcV///vfz3W/f+UrX4kTTzwx55eKxo8fH+vWrYuysrL497//HUuXLo3p06dHv379omPHjnH55Zc3eC65yCVIGvKX+fe///1o1qxZTqssb7/9dhx99NExZcqUeOaZZ2Lx4sVx7733xtVXXx2DBg3Ke98Ncdppp8ULL7wQZ555ZjzzzDOxaNGi+N3vfhd33313zm9xbd26dQwZMiQuvPDCWL58ec73W2lpaTz22GOxcOHCOisJvXv3jltvvTU++uijnGLgwgsvjCzLav/nRdeuXePaa6+NUaNG5XwMVUO99dZbcdxxx0WfPn3ipJNO2ug5NZ/jXhYsWBDjxo2L1atXx4wZM2LcuHG1q3ab06xZs5gyZUr07du39v9V9OjRo84p1xWebW67v39hMwYOHJh997vf3eRl8+fPzyIie/rpp+vdztChQ7OIqD0VFxdn3/jGN7L77rsv57ksW7YsGzFiRNalS5esRYsWWceOHbPvfe97dd5Sk8v+i4qKsnbt2mV9+/bNJk2alH3yySc57f+zt6Hm1L1795xvw+d9S96yZcuyM844I9tnn32y5s2bZ61bt84OO+yw7Jprrsnee++9Bu27Md5aePLJJ2eDBw/Oe9ym9vvaa69l+++/f3b44Ydnq1atymkbm/o+Dh8+PO99byjXtxZ+dhuLFy/OWrRokdNbC7Msy5YsWZINHTo0a9++fda8efOspKQkGzlyZPbWW2/lNH5z88jVCy+8kO21117Z//3f/2WPPvpo9r///S+bNm1a1rNnz+yrX/1qtmbNmgbt+8orr8zatWu32bfO1vjwww+zCy64IDvkkEOytm3bZrvuumvWvXv37Fe/+tVGb7msT0PfWphlWbZgwYKsX79+Wbt27bK2bdtm3/zmN7P7778/r23MnTs3i4jNPsduyuLFi7OIyHr06FHn/CVLluT8fFRZWZk1a9YsmzNnzkaXfec738mOPvroet+qvKHRo0dnvXr1yvn6FRUVm3wM1py6dOmS03Z+/OMfZ2PGjMkGDRqUFRYWZq1atcrOOeecnJ/TP/7447y/Z9ubjzBmp1ZeXh7dunWL8ePHN/ZUaIAlS5bEJZdcEtOnT4833ngjsiyLE044If74xz/WORgLtpePP/44CgsLd7oV0ibzMgFsTStXroypU6dGZWVl9O3bt7GnQwN17do1KioqYsWKFVFdXR2/+c1vYsaMGTvU2/vYuTRv3nynC4GICCsD7JSOP/74eOKJJ2Lo0KExZsyYpP5R0s5u8uTJsWrVqjjzzDPr/d8hQG7EAAAkTlYDQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOLEAAAkTgwAQOL+H27zMbDtBln2AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist = istogramma_lettere(HAMLET)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.133122Z",
     "iopub.status.busy": "2024-02-23T09:46:20.132963Z",
     "iopub.status.idle": "2024-02-23T09:46:20.135487Z",
     "shell.execute_reply": "2024-02-23T09:46:20.135188Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(' ', 30242), ('E', 17545), ('T', 13979)]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist.most_common(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.137498Z",
     "iopub.status.busy": "2024-02-23T09:46:20.137281Z",
     "iopub.status.idle": "2024-02-23T09:46:20.139958Z",
     "shell.execute_reply": "2024-02-23T09:46:20.139558Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Tra le posizioni più comuni c'è quella di 'E' che vale 4\n",
    "\n",
    "a_posizioni('E')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.142107Z",
     "iopub.status.busy": "2024-02-23T09:46:20.141851Z",
     "iopub.status.idle": "2024-02-23T09:46:20.144278Z",
     "shell.execute_reply": "2024-02-23T09:46:20.143926Z"
    }
   },
   "outputs": [],
   "source": [
    "p = semplifica(\"\"\"\n",
    "To be, or not to be, that is the question:\n",
    "Whether ’tis nobler in the mind to suffer\n",
    "The slings and arrows of outrageous fortune,\n",
    "Or to take arms against a sea of troubles,\n",
    "And by opposing end them? To die—to sleep,\n",
    "No more; and by a sleep to say we end\n",
    "The heart-ache, and the thousand natural shocks\n",
    "That flesh is heir to: ’tis a consummation\n",
    "Devoutly to be wish’d. To die, to sleep.\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.146251Z",
     "iopub.status.busy": "2024-02-23T09:46:20.145979Z",
     "iopub.status.idle": "2024-02-23T09:46:20.148234Z",
     "shell.execute_reply": "2024-02-23T09:46:20.147886Z"
    }
   },
   "outputs": [],
   "source": [
    "k = 'X'\n",
    "c = da_posizioni(orologio_somma(a_posizioni(p), a_posizioni(k)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.150192Z",
     "iopub.status.busy": "2024-02-23T09:46:20.149928Z",
     "iopub.status.idle": "2024-02-23T09:46:20.231178Z",
     "shell.execute_reply": "2024-02-23T09:46:20.230567Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist_c = istogramma_lettere(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.233031Z",
     "iopub.status.busy": "2024-02-23T09:46:20.232752Z",
     "iopub.status.idle": "2024-02-23T09:46:20.235903Z",
     "shell.execute_reply": "2024-02-23T09:46:20.235446Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[21, 14, 27]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# le tre posizioni più comuni nel testo cifrato\n",
    "\n",
    "mc = a_posizioni(''.join(c for c, n in hist_c.most_common(3)))\n",
    "mc "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.237808Z",
     "iopub.status.busy": "2024-02-23T09:46:20.237455Z",
     "iopub.status.idle": "2024-02-23T09:46:20.240680Z",
     "shell.execute_reply": "2024-02-23T09:46:20.240370Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11 FZUEHKEUXETUZEZUEHKEZNGZEOYEZNKEW␢KYZOUT\n",
      "18 ME↩LORL↩CL␢↩ELE↩LORLEUNELVDLEURLBFRDEV↩␢\n",
      "5 ↩TO␢BE␢OR␢NOT␢TO␢BE␢THAT␢IS␢THE␢QUESTION\n"
     ]
    }
   ],
   "source": [
    "for x in mc:\n",
    "  inv_k = len(SEMPLICI) + 4 - x \n",
    "  print(inv_k, a_visualizzazione(da_posizioni(orologio_somma(a_posizioni(c), [inv_k])))[:40])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.242372Z",
     "iopub.status.busy": "2024-02-23T09:46:20.242140Z",
     "iopub.status.idle": "2024-02-23T09:46:20.244745Z",
     "shell.execute_reply": "2024-02-23T09:46:20.244278Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "TO BE OR NOT TO BE THAT IS THE QUESTION\n",
      "WHETHER TIS NOBLER IN THE MIND TO SUFFER\n",
      "THE SLINGS AND ARROWS OF OUTRAGEOUS FORTUNE\n",
      "OR TO TAKE ARMS AGAINST A SEA OF TROUBLES\n",
      "AND BY OPPOSING END THEM TO DIETO SLEEP\n",
      "NO MORE AND BY A SLEEP TO SAY WE END\n",
      "THE HEARTACHE AND THE THOUSAND NATURAL SHOCKS\n",
      "THAT FLESH IS HEIR TO TIS A CONSUMMATION\n",
      "DEVOUTLY TO BE WISHD TO DIE TO SLEEP\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 5 è la chiave inversa che funziona! \n",
    "\n",
    "print(da_posizioni(orologio_somma(a_posizioni(c), [5])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Crittografia a chiave asimmetrica\n",
    "\n",
    "Per prima cosa proviamo a capire come fare a tradurre un testo in un intero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.246432Z",
     "iopub.status.busy": "2024-02-23T09:46:20.246248Z",
     "iopub.status.idle": "2024-02-23T09:46:20.248906Z",
     "shell.execute_reply": "2024-02-23T09:46:20.248543Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[115, 104, 97, 108, 108, 32, 100, 111]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = 'shall do'\n",
    "a_bytes(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comportiamoci come se fosse un numero in base 256"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.250610Z",
     "iopub.status.busy": "2024-02-23T09:46:20.250382Z",
     "iopub.status.idle": "2024-02-23T09:46:20.253251Z",
     "shell.execute_reply": "2024-02-23T09:46:20.252833Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8316003830238045295"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num = 0\n",
    "for b in a_bytes(p):\n",
    "  num = num * 256 + b\n",
    "m = num\n",
    "m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Al contrario con moduli e divisioni, possiamo recuperare i byte ­— ma dobbiamo girare il risultato finale!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.254912Z",
     "iopub.status.busy": "2024-02-23T09:46:20.254737Z",
     "iopub.status.idle": "2024-02-23T09:46:20.257710Z",
     "shell.execute_reply": "2024-02-23T09:46:20.257300Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[115, 104, 97, 108, 108, 32, 100, 111]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = []\n",
    "while num > 0:\n",
    "  b.append(num % 256)\n",
    "  num = num // 256\n",
    "b[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per costruire le chiavi privata e pubblica ci vogliono 2 primi grandi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.259312Z",
     "iopub.status.busy": "2024-02-23T09:46:20.259145Z",
     "iopub.status.idle": "2024-02-23T09:46:20.261223Z",
     "shell.execute_reply": "2024-02-23T09:46:20.260815Z"
    }
   },
   "outputs": [],
   "source": [
    "p = 1000000005713\t\n",
    "q = 1000000005721\n",
    "n = p * q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si può scegliere $e$ anche molto piccola, ma deve essere coprima con $\\varphi(n)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.262932Z",
     "iopub.status.busy": "2024-02-23T09:46:20.262702Z",
     "iopub.status.idle": "2024-02-23T09:46:20.264791Z",
     "shell.execute_reply": "2024-02-23T09:46:20.264405Z"
    }
   },
   "outputs": [],
   "source": [
    "φ = (p - 1) * (q - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.266515Z",
     "iopub.status.busy": "2024-02-23T09:46:20.266287Z",
     "iopub.status.idle": "2024-02-23T09:46:20.269174Z",
     "shell.execute_reply": "2024-02-23T09:46:20.268773Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# cerco un e che sia coprimo con φ\n",
    "\n",
    "for e in range(3, φ):\n",
    "  if MCD(e, φ) == 1: break\n",
    "e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora si può ricavare $d$ calcolando l'inverso di $e$ modulo $\\varphi(n)$ (chiamaremo `Mφ` questo modulo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.270885Z",
     "iopub.status.busy": "2024-02-23T09:46:20.270658Z",
     "iopub.status.idle": "2024-02-23T09:46:20.273500Z",
     "shell.execute_reply": "2024-02-23T09:46:20.273092Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "428571433470857156859703"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calcolo d\n",
    "\n",
    "Mφ = Mod(φ)\n",
    "d = (Mφ[e] ** (-1)).rappresentante()\n",
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cifriamo e decifriamo con le chiavi pubblica e privata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.275221Z",
     "iopub.status.busy": "2024-02-23T09:46:20.274998Z",
     "iopub.status.idle": "2024-02-23T09:46:20.277693Z",
     "shell.execute_reply": "2024-02-23T09:46:20.277287Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, True)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MCD(m, n) == 1, m < n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora abbiamo bisogno di ragonare modulo $n$, chiamiamo `Mn` questo modulo, da non confondere con `Mφ`!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.279485Z",
     "iopub.status.busy": "2024-02-23T09:46:20.279268Z",
     "iopub.status.idle": "2024-02-23T09:46:20.282266Z",
     "shell.execute_reply": "2024-02-23T09:46:20.281778Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[580701743569890406626285]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mn = Mod(n)\n",
    "\n",
    "Mn[m] ** e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.284092Z",
     "iopub.status.busy": "2024-02-23T09:46:20.283805Z",
     "iopub.status.idle": "2024-02-23T09:46:20.286597Z",
     "shell.execute_reply": "2024-02-23T09:46:20.286226Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8316003830238045295]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mn[580701743569890406626285] ** d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-02-23T09:46:20.288341Z",
     "iopub.status.busy": "2024-02-23T09:46:20.288044Z",
     "iopub.status.idle": "2024-02-23T09:46:20.290574Z",
     "shell.execute_reply": "2024-02-23T09:46:20.290274Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8316003830238045295"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  }
 ],
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